Kneser's theorem (combinatorics)

Restricted results

Stronger results are known for restricted classes of polynomials or algebraic numbers.

If P(x) is not reciprocal then

$M(P)\geq M(x^{3}-x-1)\approx 1.3247$

and this is clearly best possible. If further all the coefficients of P are odd then

$M(P)\geq M(x^{2}-x-1)\approx 1.618.$

If the field Q(α) is Galois over Q then Lehmer's conjecture holds.

References

• Smyth, Chris (2008). "The Mahler measure of algebraic numbers: a survey". In McKee, James; Smyth, Chris (eds.). Number Theory and Polynomials. London Mathematical Society Lecture Note Series. Vol. 352. Cambridge University Press. pp. 322–349. ISBN 978-0-521-71467-9.